Problem: Given $ m \angle MON = 7x + 3$, and $ m \angle LOM = 3x + 67$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 67} + {7x + 3} = {180}$ Combine like terms: $ 10x + 70 = 180$ Subtract $70$ from both sides: $ 10x = 110$ Divide both sides by $10$ to find $x$ $ x = 11$ Substitute $11$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 3({11}) + 67$ Simplify: $ {m\angle LOM = 33 + 67}$ So ${m\angle LOM = 100}$.